<div>Gas turbine engines have operated on the Brayton cycle for decades, each decade only gaining approximately one to two percent in thermal efficiency as a result of efforts</div><div>to improve engine performance. Pressure-gain combustion in place of constant-pressure combustion in a Brayton cycle could provide a drastic step-change in the thermal efficiency of these devices, leading to reductions in fuel consumption and emissions production. Rotating Detonation Engines (RDEs) have been widely researched as a viable option for pressure-gain combustion. Due to the extremely high frequencies associated with operation of an RDE, the development and application of high-speed diagnostics techniques for RDEs is necessary to further understand and</div><div>develop these devices.</div><div><br></div><div>An application of high-speed diagnostic techniques in a natural gas-air RDE at conditions relevant to land-based power generation is presented. Diagnostics included high-frequency chamber pressure measurements, chemiluminescence imaging of the annulus, and Particle Image Velocimetry (PIV) measurements at the exit plane of the RDE. Results from a case with two detonation waves rotating clockwise (aft looking forward) in the combustor annulus are presented. Detonation surface plots are created from chemiluminescence images and allow for the extraction of properties such as dominant frequency modes and wave number, speed, and direction. The chamber frequency for the case with two co-rotating waves in the chamber is found to be 3.46 kHz and corresponds to average individual wave speeds of 68% Chapman-Jouguet (CJ) velocity. Dynamic Mode Decomposition (DMD) is applied and indicates the presence of two strong detonation waves rotating clockwise and periodically intersecting with weaker, counter-rotating waves in the annulus at certain times during operation. Singular-Spectrum Analysis (SSA) is used to isolate modes corresponding to the detonation frequency in the signals of velocity components obtained from PIV, maintaining instantaneous phase information. Axial and azimuthal components of velocity are observed to remain nearly 180 degrees out of phase. Lastly, approximate angles for the trailing oblique shocks in the combustion chamber are calculated.</div>

<div>Rotating Detonation Engines (RDEs) provide a promising avenue for reducing greenhouse gas emissions from combustion-based propulsion and power systems by improving their thermodynamic efficiency through the application of pressure-gain combustion. However, the thermodynamic and systems-level advantages remain unrealized due to the challenge of harnessing the tightly coupled physics and nonlinear detonation dynamics inherent to RDEs, particularly for the less-detonable reactants characteristic of applications. Therefore, a RDE was developed to operate with natural gas and air as the primary reactants at elevated chamber pressures and air preheat temperatures, providing a platform to study RDEs with the less-detonable reactants and flow conditions representative of land-based power generation gas turbine engines. The RDE was tested with two injector configurations in a broad, parametric survey of flow conditions to determine the effect of operating parameters on the propagation of detonation waves in the combustor and delivered performance. Measurements of chamber wave dynamics were performed using high-frequency pressure transducers and high-speed imaging of broadband combustion chemiluminescence, while thrust measurements were used to characterize the work output potential.</div><div><br></div><div>The detonation dynamics were first studied to characterize RDE operability for the target application. Wave propagation speeds of up to 70% of the mixture Chapman-Jouguet detonation velocity and chamber pressure fluctuations greater than 4 times the mean chamber pressure were observed. Supplementing the air with additional oxygen, varying the equivalence ratio, and enriching the fuel with hydrogen revealed that combustor operability is sensitive to the chemical kinetics of the reactant mixture. While most test conditions exhibited counter-rotating detonation waves within the chamber, one injector design was able to support single wave propagation. A thermodynamic performance model was developed to aid analysis of RDE performance by making comparisons of net pressure gain for identical flow conditions. While the injector that supported a single wave operating mode better followed the trends predicted by the model, neither injector achieved the desire stagnation pressure gain relative to the reactant manifold pressure. Application of the model to a generic RDE revealed the necessity of normalizing any RDE performance parameter by the driving system potential and identified the area ratio between the exhaust and injection throats as the primary parameter affecting delivered pressure gain. A pair of test conditions with distinct wave dynamics were selected from the parametric survey to qualitatively and quantitatively analyze the exhaust flow using high-speed particle image velocimetry. A single detonation wave with an intermittent counter-rotating wave was characterized in the first test case, while a steady counter-rotating mode was studied in the second. The velocity measurements were phase averaged with respect to the instantaneous wave location to reveal contrasting flowfields for the two cases. The total pressure and temperature of flow exiting the combustor were computed using the phase-resolved velocity measurements along with the measured reactant flowrate and thrust to close the global balance of mass and momentum, providing an improved method of quantifying RDE performance. Finally, a reduced order model for studying RDE operability and mode selection was developed. The circumferential detonation wave dynamics are simulated and permitted to naturally evolve into the quasi-steady state operating modes observed in RDEs. Preliminary verification studies are presented and areas for further development are identified to enable the model to reach a broader level of applicability.</div><div><br></div><div>The experimental component of this work has advanced understanding of RDE operation with less-detonable reactants and developed improved methods for quantifying RDE performance. The accompanying modeling has elucidated the design parameters and flow conditions that influence RDE performance and provided a framework to investigate the factors that govern RDE mode selection and operability.<br></div>

<p>The interaction and behavior of detonation waves propagating in a linear detonation combustor (LDC) were studied to identify the coupled thermoacoustic-chemical phenomenon responsible for self-generated and self-sustained detonation waves. The LDC was operated with natural gas and gaseous oxygen over a wide range of equivalence ratios and optically observed with OH*-chemiluminescence, schlieren, and broadband imaging in addition to high-frequency pressure transducers and photomultiplier tubes. Counter-propagating, self-sustained detonation waves were observed in the semi-bounded combustor to accelerate and amplify consistently from the closed-boundary to the open-boundary. The incident waves then reflect off of the open-boundary and transition into weaker waves that propagate acoustically relative to the burned products before being reflected by the closed-boundary and accelerating to dominancy once again. The combustor was then modified to have symmetric boundary conditions with both ends closed. For closed cases, the detonation waves experienced similar acceleration and amplification processes. The incident waves accelerate until they are reflected by a closed boundary into a flow field for which the fuel-injectors have yet to recover. For this reason, the reflected waves propagate through burned products until they encounter fresh reactants and accelerate again. The closed boundary conditions also caused the direction of dominance to periodically alternate. This study indicates that the local mixing field between open and closed boundary conditions affects the strength and speed of the reflected wave and demonstrates the impact of combustor geometry on coupled thermoacoustic-chemical phenomenon in RDEs.</p>

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Pressure Gain Combustion (PGC) systems have gained significant focus in recent years due to its potential for increased thermodynamic efficiency over a constant pressure cycle (or Brayton cycle). A rotating detonation combustor (RDC) is a type of PGC system, which is thermodynamically more efficient than the conventional gas turbine combustor. One of the main aspects of the detonation process is the rapid burning of the fuel-oxidizer mixture, due to which there is not enough time for the pressure to equilibrate. Therefore, the process is thermodynamically closer to a constant volume process, which is thermodynamically more efficient than a constant pressure cycle. RDC, if integrated successfully with a turbine, can increase thermal efficiency and reduce carbon emissions, especially when hydrogen is introduced into the fuel stream. However, due to highly unsteady flow generated from RDC, a systematic approach to transition the flow exiting the RDC to supply steady, subsonic flow at the turbine inlet has not been developed so far. Numerical simulations serve as a valuable tool to provide insight into the flow physics and to optimize the RDE design. Numerical studies have explored RDC by utilizing high-fidelity 3D simulations. However, these CFD studies require significant computational resources, due to the large differences in length and time scales between the flow field and the chemical reactions involved. The motivation of this dissertation is to investigate these research gaps and to develop computationally efficient methods for RDC designs to be integrated with downstream turbine section. First, this research work develops a methodology to predict the unsteady flow field exiting an RDC using 2D reacting simulations and to validate the approach using experimental measurements. Next, computational techniques are applied to condition the flow within the annulus by strategically constricting the flow area. A design of experiment (DoE) study is used to optimize the area profiling of the combustor. Additionally, the performance of the profiled design is compared against the baseline and the conventional nozzle design used in the literature. However, these numerical works use a perfectly premixed condition, whereas, the actual setup consists of discrete fuel/oxidizer injectors providing a non-uniform mixture in the combustor. To eliminate the assumption of perfectly premixed conditions, a method is developed to model the dynamic injector response of fuel/oxidizer plenums. The goal of this approach is to provide an inhomogeneous mixture composition without having to resolve/mesh the individual injectors. This research work provides a robust and computationally efficient methods for minimizing unsteadiness, maximizing pressure gain, and modeling dynamic injector response of an RDC. / Doctor of Philosophy / Traditional gas turbine combustor utilizes deflagration combustion. In recent years, detonation-based combustion has been explored as an alternative to enhance the efficiency of a modern gas turbine combustor. Rotating Detonation Combustor (RDC) utilizes detonation-based combustion and is thermodynamically efficient compared to conventional gas turbine combustors. The RDC consists of a detonation wave front and an oblique shock wave, which travel towards the exit of the combustor. Thus, the flow exiting the RDC is highly unsteady. The turbine requires a relatively steady flow at the inlet guide vanes. Therefore, the flow exiting the RDC needs to be conditioned before integrating with a downstream turbine section to gain the thermodynamic benefits of RDC. Numerical simulation of an RDC provides additional flexibility over experiments in understanding the flow physics. In addition, simulations are vital in optimizing the RDC designs such that the flow exiting the combustor is relatively uniform without comprising the pressure gain benefits of RDC. However, one of the challenges is that the RDC simulations are computationally expensive. Therefore, computationally efficient methods are required to understand and optimize the RDC designs to minimize the unsteady flow behavior and maximize the pressure gain. The objective is to utilize 2D and 3D reacting simulations to understand the flow behavior and to develop an optimization workflow to condition the flow exiting the combustor. Additionally, the optimized design is evaluated against the baseline and the conventional design used previously in the literature. Moreover, in most RDCs, the fuel and oxidizer are injected using discrete injectors. Due to the discrete injection, the fuel/oxidizer mixture is never perfectly premixed and results in a localized variation in fuel-oxidizer composition in the combustor. A novel method is developed to model the dynamic injector response of discrete fuel/oxidizer injection. The goal is to provide an inhomogeneous mixture composition without having to resolve/mesh the individual injectors. The emphasis of this study is to provide insight into the importance of flow conditioning exiting the RDC and the development of efficient CFD methods to optimize RDC to seamlessly integrate with a downstream turbine section.

The advent of detonation-based propulsion systems represents an opportunity for more sustainable combustion processes and hypersonic travel. In regular detonations, some yet to be resolved instabilities are attributed to the propagation and collision of triple points, formed at the intersection of a Mach stem, an incident shock and a transverse wave. Over time, the tracks observed by these points form a structure made of diamond-shaped cells. Ultimately, The ability to sustain these instabilities plays a key role in the propagation of detonations. The present work unveils the dynamics of gaseous detonations at a sub-cellular level. The experiments are conducted with hydrogen fuel which is of great potential for detonation engine applications. The hydrogen-oxygen mixtures are held at stoichiometry and the nitrogen dilution in oxygen is varied from 30% to 70%. This allows to observe the effects of activation energy through the dilution on the sub-cellular wave dynamics. Measurements of cell sizes and wave velocity are reported through shadowgraph imaging. A new methodology is developed for the simultaneous resolution of the velocity field and cellular structure. The statistical analysis is made possible due to the design of a fully automated detonation facility. The experiments are conducted in a thin channel to minimize gradients in the third direction and confine the detonation cells to a plane. The results in cell sizes are in good agreement with the literature and expand the conditions reported thus far. Local observations of the velocity within the cells are used to explain the regularity of the overall wave speed, found to increase at lower dilution. Lastly, high fidelity simulations are conducted to model the cellular structure in hydrogen-air oblique detonation waves. Similarly to the experiments, the velocity field is extracted along the detonation cells and reveals the effects of wave curvature on triple point dynamics.

Pressure gain combustion is a form of combustion that uses pressure waves to transfer energy and generate a rise in total pressure during the combustion process. Pressure gain combustion shows potential to increase the cycle efficiency of conventional gas turbine engines if used in place of the steady combustor. However, one of the challenges of integrating pressure gain combustion into a gas turbine engine is that a turbine driven by pulsing flow experiences a decrease in efficiency. The interaction of pressure pulses with a turbine was investigated to gain physical insights and to provide guidelines for designing turbines to be driven by pulsing flow. An experimental rig was built to compare steady flow with pulsing flow. Compressed air was used in place of combustion gases; pressure pulses were created by rotating a ball valve with a motor. The data showed that a turbine driven by full annular pressure pulses has a decrease in turbine efficiency and pressure ratio. The average decrease in turbine efficiency was 0.12 for 10 Hz, 0.08 for 20 Hz, and 0.04 for 40 Hz. The turbine pressure ratio, defined as the turbine exit total pressure divided by the turbine inlet total pressure, ranged from 0.55 to 0.76. The average decrease in turbine pressure ratio was 0.082 for 10 Hz, 0.053 for 20 Hz, and 0.064 for 40 Hz. The turbine temperature ratio and specific turbine work were constant. Pressure pulse amplitude, not frequency, was shown to be the main cause for the decrease in turbine efficiency. Computational fluid dynamics simulations were created and were validated with the experimental results. Simulations run at the same conditions as the experiments showed a decrease in turbine efficiency of 0.24 for 10 Hz, 0.12 for 20 Hz, and 0.05 for 40 Hz. In agreement with the experimental results, the simulations also showed that pressure pulse amplitude is the driving factor for decreased turbine efficiency and not the pulsing frequency. For a pulsing amplitude of 86.5 kPa, the efficiency difference between a 10 Hz and a 40 Hz simulation was only 0.005. A quadratic correlation between turbine efficiency and corrected pulse amplitude was presented with an R-squared value of 0.99. Incidence variation was shown to cause the change in turbine efficiency and a correlation between corrected incidence and corrected amplitude was established. The turbine geometry was then optimized for pulsing flow conditions. Based on the optimization results and observations, design recommendations were made for designing turbines for pulsing flow. The first design recommendation was to weight the design of the turbine toward the peak of the pressure pulse. The second design recommendation was to consider the range of inlet angles and reduce the camber near the leading edge of the blade. The third design recommendation was to reduce the blade turning to reduce the wake caused by pulsing flow. A new turbine design was created and tested following these design recommendations. The time-accurate validation simulation for a 10 Hz pressure pulse showed that the new turbine decreased the entropy generation by 35% and increased the efficiency by 0.04 (5.4%).